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solve_eoldas_spatial.py
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solve_eoldas_spatial.py
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#!/usr/bin/env python
import pdb
import numpy as np
def gauss_kern(size, sizey=None):
"""
Returns a normalized 2D gauss kernel array for convolutions
From http://www.scipy.org/Cookbook/SignalSmooth
"""
import numpy as np
size = int(size)
if not sizey:
sizey = size
else:
sizey = int(sizey)
x, y = np.mgrid[-size:size+1, -sizey:sizey+1]
g = np.exp(-(x**2/float(size)+y**2/float(sizey)))
return g / g.sum()
def create_data ( nr,nc,n_per=1, noise=0.15, obs_off=0.33, \
window_size=3):
"""
Create synthetic "NDVI-like" data for a fictitious space series. We return
the original data, noisy data (using IID Gaussian noise), the QA flag as well
as the time axis.
Missing observations are simulated by drawing a random number between 0 and 1
and checking against obs_off.
Parameters
----------
nc : number of columns
nr : number of rows
n_per : integer
Observation periodicity. By default, assumes every sample
noise : float
The noise standard deviation. By default, 0.15
obs_off : float
The threshold to decide on missing observations in the series.
"""
import numpy as np
from scipy import signal
r,c = np.mgrid[1:nr+1:n_per,1:nc+1:n_per]
ndvi_clean = np.clip(np.sin(np.pi*2*(r-1)/nr)*np.sin(np.pi*2*(c-1)/nc), 0,1)
ndvi = ndvi_clean.copy()
# add Gaussian noise of sd noise
ndvi = np.random.normal(ndvi,noise,ndvi.shape)
# set the qa flags for each sample to 1 (good data)
qa_flag = np.ones_like ( ndvi).astype( np.int32 )
passer = np.random.rand(ndvi.shape[0],ndvi.shape[1])
if window_size >0:
# force odd
window_size = 2*(window_size/2)+1
# smooth passer
g = gauss_kern(window_size)
passer = signal.convolve(passer,g,mode='same')
# assign a proportion of the qa to 0 from an ordering of the smoothed
# random numbers
qf = qa_flag.flatten()
qf[np.argsort(passer,axis=None)[:passer.size * obs_off]] = 0
qa_flag = qf.reshape(passer.shape)
return ( r,c , ndvi_clean, ndvi, qa_flag )
def prepare(nr=50,nc=100,noise=0.15,n_per=1,obs_off=0.33,model_order=1,\
filtwindow=3):
import os,tempfile
# Start by creating some univarite time series data
( r, c, ndvi_clean, ndvi, qa_flag ) = \
create_data ( nr,nc,n_per=n_per, noise=noise, \
obs_off=obs_off,\
window_size=filtwindow)
# calculate the gradient of the ndvi
dydx = np.gradient(ndvi_clean.flatten())/np.gradient(c.flatten())
# to the model_order-th order
for i in np.arange(1,model_order):
dydx = np.gradient(dydx)
# calculate the 'true' gamma
model_unc = np.sqrt(np.mean(dydx**2))
gamma = 1./model_unc
temp, fp_brf = tempfile.mkstemp()
os.write (temp, \
"#PARAMETERS mask row col NDVI sd-NDVI\n")
[ os.write (temp,"%d %f %f %f %f\n" % \
( int(qa_flag.flatten()[i]), r.flatten()[i], c.flatten()[i], \
ndvi.flatten()[i], noise)) \
for i in xrange (len(ndvi.flatten()))]
os.close(temp)
return fp_brf,gamma,r,c,ndvi_clean,ndvi,qa_flag
if __name__ == "__main__":
import sys,tempfile
this = sys.argv[0]
import eoldas
# SD of noise
noise=0.15
# nominal sampling period
n_per=1
# proportion of missing samples
obs_off=0.333
# order of differential model (integer)
model_order=1
# sgwindow is larger to create larger data gaps
filtwindow=13
# set up data for this experiment
file, ideal_gamma,r,c,ndvi_clean,ndvi,qa_flag = \
prepare(noise=noise,n_per=n_per,\
obs_off=obs_off,model_order=model_order,\
filtwindow=filtwindow)
# set gamma to less than the the theoretical value
gamma = ideal_gamma*0.2
# set op file names
xfile = 'output/Identity/NDVI_Identity_spatial.params'
yfile = 'output/Identity/NDVI_fwd_spatial.params'
# initialise optuions for DA overriding any in config files
cmd = 'eoldas_run.py ' + \
' --conf=config_files/eoldas_config.conf --conf=config_files/IdentitySpatial.conf ' + \
' --logfile=mylogs/IdentitySpatial.log ' + \
' --calc_posterior_unc ' + \
' --parameter.solve=0,0,1 ' + \
' --parameter.result.filename=%s '%xfile +\
' --parameter.x.default=%f,%f,0.0 '%(gamma,gamma) + \
' --operator.obs.y.result.filename=%s'%yfile +\
' --operator.obs.y.state=%s'%file+\
' --parameter.x.state=%s'%file+\
' --operator.modelr.rt_model.model_order=%d '%model_order +\
' --operator.modelc.rt_model.model_order=%d '%model_order
# initialise eoldas
self = eoldas.eoldas(cmd)
# solve DA
self.solve(write=True)
# ok, now read the results back in
fwd = (np.array([i.split() for i in open(xfile).readlines()[1:]]).astype(float))
fwdndvi = fwd[:,5].reshape(ndvi_clean.shape)
fwdndvisd = fwd[:,8].reshape(ndvi_clean.shape)
import pylab as plt
plt.clf()
plt.xlabel('original ndvi')
plt.ylabel('modelled ndvi')
plt.xlim(0,1)
plt.ylim(0,1)
plt.plot([0,1],[0.,1.],'k')
#plt.plot(ndvi[qa_flag].flatten(),fwdndvi[qa_flag].flatten(),'r.',label='fwd at obs')
plt.errorbar(ndvi_clean.flatten(),fwdndvi.flatten(),yerr=fwdndvisd.flatten()*1.96,fmt='g.')
plt.plot(ndvi_clean.flatten(),fwdndvi.flatten(),'r.')
#plt.plot(ndvi_clean.flatten(),fwdndvi.flatten(),'g.',label='fwd')
plt.savefig('%s.png'%xfile)
plt.clf()
plt.xlabel('original ndvi')
plt.ylabel('modelled ndvi')
plt.plot([0,1],[0.,1.],'k')
plt.xlim(0,1)
plt.ylim(0,1)
#plt.plot(ndvi[qa_flag].flatten(),fwdndvi[qa_flag].flatten(),'r.',label='fwd at obs')
plt.errorbar(ndvi_clean.flatten(),fwdndvi.flatten(),yerr=fwdndvisd.flatten()*1.96,fmt='g.')
plt.plot(ndvi_clean.flatten(),fwdndvi.flatten(),'r.')
plt.errorbar(ndvi[qa_flag].flatten(),fwdndvi[qa_flag].flatten(),\
yerr=(fwdndvisd[qa_flag].flatten()*1.96),xerr=(fwdndvisd[qa_flag].flatten()*0+noise*1.96),fmt='b.')
plt.plot(ndvi[qa_flag].flatten(),fwdndvi[qa_flag].flatten(),'g.')
plt.xlim(0,1.0)
plt.ylim(0,1.0)
plt.savefig('%s_withdata.png'%xfile)
plt.clf()
plt.imshow(ndvi_clean,interpolation='nearest',vmin=-1,vmax=1)
plt.colorbar()
plt.savefig('%s_clean.png'%xfile)
plt.clf()
plt.imshow(fwdndvisd,interpolation='nearest',vmin=0,vmax=0.15)
plt.colorbar()
plt.savefig('%s_fwdsd.png'%xfile)
plt.clf()
plt.imshow(fwdndvi,interpolation='nearest',vmin=-1,vmax=1)
plt.colorbar()
plt.savefig('%s_fwd.png'%xfile)
plt.clf()
xx = ndvi.copy()
xx[(1-qa_flag).astype(bool)] = -1
plt.imshow(xx,interpolation='nearest',vmin=-1,vmax=1)
plt.colorbar()
plt.savefig('%s_data.png'%xfile)
plt.clf()
x = np.arange(len(fwdndvi[13])) + 1
plt.plot(x,ndvi_clean[13],label='clean')
plt.plot(x,xx[13],'.',label='data')
plt.plot(fwdndvi[13],label='fwd')
plt.ylim(-0.1,1)
plt.errorbar(x,fwdndvi[13],yerr=(fwdndvisd[13]))
plt.xlabel('column')
plt.ylabel('ndvi')
plt.legend()
plt.savefig('%s_transect.png'%xfile)